Temperature dependence of viscoelastic behaviour

Previously we have referred only indirectly to the effect of temperature on viscoelastic behaviour. From a practical viewpoint, however, the temperature dependence of polymer properties is of paramount importance because plastics and rubbers show very large changes in properties with changing temperature. 

In purely scientific terms, the temperature dependence has two primary points of interest. In the first place, as we have seen in Chapter 5, it is not possible to obtain from a single experimental technique a complete range of measuring frequencies to evaluate the relaxation spectrum at a single temperature. It is therefore a matter of considerable experimental convenience to change the temperature of the experiment, and so bring the relaxation processes of interest within a time-scale that is readily available. This procedure, of course, assumes that a simple interrelation exists between time-scale and temperature, and we will discuss shortly the extent to which this assumption is justified. 

The molecular physicist is interested in understanding how this conformational freedom is achieved in terms of molecular motions, for example to establish which bonds in the structure become able to rotate as the temperature is raised. One approach, which has proved successful to some degree, has been to compare the viscoelastic behaviour with dielectric relaxation behaviour and more particiflarly with nuclear magnetic resonance behaviour. 

In addition, there is one primary transition, usually called the glass transition . 

In addition, there is one primary transition, usually called the glass transition , that involves a large change in modulus. The temperature at which it occurs is commonly denoted by Tg. 

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Free vibration methods suffer from the disadvantage that the frequency of vibration depends on the stiffness of the specimen, which varies with temperature, so that forced vibration methods are to be preferred when the frequency and temperature dependence of viscoelastic behaviour are to be investigated. 

The simplest theories that attempt to deal with the temperature dependence of viscoelastic behaviour are the transition state or barrier theories [9,10]. The site model was originally developed to explain the dielectric behaviour of solids [11,12], but was later applied to mechanical relaxations in polymers [13]. 

Ferry, J. D. (1980). Dependence of viscoelastic behaviour on temperature and pressure. In Viscoelastic properties of polymers. NewYork Wiley, 260-264. 

For the investigation of the time and the temperature dependence of the fibre strength it is necessary to have a theoretical description of the viscoelastic tensile behaviour of polymer fibres. Baltussen has shown that the yielding phenomenon, the viscoelastic and the plastic creep of a polymer fibre, can be described by the Eyring reduced time (ERT) model [10]. The shear deformation of a domain brings about a mutual displacement of adjacent chains, the... 

For a Newtonian fluid, the shear stress is proportional to the shear rate, the constant of proportionality being the coefficient of viscosity. The viscosity is a property of the material and, at a given temperature and pressure, is constant. Non-Newtonian fluids exhibit departures from this type of behaviour. The relationship between the shear stress and the shear rate can be determined using a viscometer as described in Chapter 3. There are three main categories of departure from Newtonian behaviour behaviour that is independent of time but the fluid exhibits an apparent viscosity that varies as the shear rate is changed behaviour in which the apparent viscosity changes with time even if the shear rate is kept constant and a type of behaviour that is intermediate between purely liquid-like and purely solid-like. These are known as time-independent, time-dependent, and viscoelastic behaviour respectively. Many materials display a combination of these types of behaviour. 

The viscoelastic nature of polymers generally determines rate and temperature dependence of their mechanical properties. At low strain levels, i.e. in a linear regime, this dependence is well described by intrinsic material properties defined within constitutive viscoelastic laws [1]. At high strains, in presence of failure processes, such as yielding or fracture, it is more difficult to establish a constitutive behaviour as well as to define material properties able to intrinsically characterise the failure process and its possible viscoelastic features. 

Ideal yielding behaviour is approached by many glassy polymers well below their glass-transition temperatures, but even for these polymers the stress-strain curve is not completely linear even below the yield stress and the compliance is relatively high, so that the deformation before yielding is not negligible. Further departures from ideality involve a strain-rate and temperature dependence of the yield stress. These two features of behaviour are, of course, characteristic of viscoelastic behaviour. 

Many results of the dependence of viscoelastic and calorimetric behaviour on electrolyte concentration are reported by Nishinari et al. [579,588-592]. These authors defined [588] the sol-gel transition temperature, T b of gellan solutions as the temperature where, in a cxxrling experiment, the storage modulus starts to deviate from the ba.sc line see Fig. 241). In comparison with the method of the... 

The temperature dependence of viscosity of a soda lime silicate glass (Fig. 1.11) was already discussed previously and its relevance to glass processing, especially to obtain stress-free glass products was also explained. The viscoelastic behaviour of glasses can be described by Newton s (1.2) and Maxwell s law (1.4). Very comprehensive reviews of the subject matter have been published by Scholze [450] and Bruckner et al. [74]. Pye et al. [414] give tables which allow for calculation the viscosity of glass melts in dependence on composition and temperature. 

Throughout this chapter the viscoelastic behaviour of plastics has been described and it has been shown that deformations are dependent on such factors as the time under load and the temperature. Therefore, when structural components are to be designed using plastics, it must be remembered that the classical equations which are available for the design of springs, beams, plates, cylinders, etc., have all been derived under the assumptions that... 

Thus, one may conclude that, in the region of comparatively low frequencies, the schematic representation of the macromolecule by a subchain, taking into account intramolecular friction, the volume effects, and the hydrodynamic interaction, make it possible to explain the dependence of the viscoelastic behaviour of dilute polymer solutions on the molecular weight, temperature, and frequency. At low frequencies, the description becomes universal. In order to describe the frequency dependence of the dynamic modulus at higher frequencies, internal relaxation process has to be considered as was shown in Section 6.2.4. 

These are essentially independent effects a polymer may exhibit all or any of them and they will all be temperature-dependent. Section 6.2 is concerned with the small-strain elasticity of polymers on time-scales short enough for the viscoelastic behaviour to be neglected. Sections 6.3 and 6.4 are concerned with materials that exhibit large strains and nonlinearity but (to a good approximation) none of the other departures from the behaviour of the ideal elastic solid. These are rubber-like materials or elastomers. Chapter 7 deals with materials that exhibit time-dependent effects at small strains but none of the other departures from the behaviour of the ideal elastic sohd. These are linear viscoelastic materials. Chapter 8 deals with yield, i.e. non-recoverable deformation, but this book does not deal with materials that exhibit non-linear viscoelasticity. Chapters 10 and 11 consider anisotropic materials. 

The relaxations that lead to viscoelastic behaviour are the result of various types of molecular motions, some of which are described in section 5.7, and they occur more rapidly at higher temperature. The compliance /(/), for instance, is therefore a function of temperature, T, which means that it should really be written as J t, T). Suppose that the effect of a rise in temperature from some chosen standard temperature To is to speed up every stage in a relaxation process by a constant factor that depends on the new temperature T. This is equivalent to saying that the interval of time required for any small change in strain to take place is divided by a factor uj- that depends on T and has the value 1 when T = T . This means that, if measured values of J(t, T) are plotted against ta-r, curves for all temperatures should be superposed. Similarly, if values of J co, T) are plotted against curves for all temperatures should be superposed on the curve for T. ... 

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